Probing many-body systems
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T. Kitagawa (Harvard), S. Pielawa (Harvard), D. Pekker (Harvard), R. Sensarma (Harvard/JQI), V. Gritsev (Fribourg), M. Lukin (Harvard), PowerPoint PPT Presentation


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Probing many-body systems of ultracold atoms. Harvard-MIT. $$ NSF, MURI, DARPA, AFOSR. Eugene Demler Harvard University. T. Kitagawa (Harvard), S. Pielawa (Harvard), D. Pekker (Harvard), R. Sensarma (Harvard/JQI), V. Gritsev (Fribourg), M. Lukin (Harvard), Lode Pollet (Harvard).

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T. Kitagawa (Harvard), S. Pielawa (Harvard), D. Pekker (Harvard), R. Sensarma (Harvard/JQI), V. Gritsev (Fribourg), M. Lukin (Harvard),

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T kitagawa harvard s pielawa harvard d pekker harvard r sensarma harvard

Probing many-body systems of ultracold atoms

Harvard-MIT

$$ NSF, MURI, DARPA, AFOSR

Eugene Demler Harvard University

T. Kitagawa (Harvard), S. Pielawa (Harvard),

D. Pekker (Harvard), R. Sensarma (Harvard/JQI),

V. Gritsev (Fribourg), M. Lukin (Harvard),

Lode Pollet (Harvard)

Collaboration with experimental groups of

T. Esslinger, I. Bloch, J. Schmiedmayer


Outline

Outline

  • Lattice modulation

  • experiments with

  • fermions

  • Ramsey interference

  • experiments in 1d

Also yesterday’s talks by Henning Moritz and Andreas Ruegg


Lattice modulation experiments with fermions in optical lattice

Lattice modulation experiments with fermions in optical lattice.

Probing the Mott state of fermions

Expts: Joerdens et al., Nature (2008)

Greif, Tarruell, Strohmaier, Moritz, Esslinger et al.

Theory: Kollath et al., PRA (2006)

Huber, Ruegg, PRA (2009)

Sensarma et al. PRL 2009

Pollet, Pekker, Demler, unpublished

Yesterday’s talks by Henning Moritz and Andreas Ruegg


T kitagawa harvard s pielawa harvard d pekker harvard r sensarma harvard

Modulate lattice potential

Lattice modulation experiments

Probing dynamics of the Hubbard model

Measure number of doubly

occupied sites

Main effect of shaking: modulation of tunneling

Doubly occupied sites created when frequency w matches Hubbard U


T kitagawa harvard s pielawa harvard d pekker harvard r sensarma harvard

Lattice modulation experiments

Probing dynamics of the Hubbard model

R. Joerdens et al., Nature 455:204 (2008)


T kitagawa harvard s pielawa harvard d pekker harvard r sensarma harvard

Mott gap for the charge forms at

Antiferromagnetic ordering at

Mott state

Regime of strong interactionsU>>t.

“High” temperature regime

All spin configurations are equally likely.

Can neglect spin dynamics.


T kitagawa harvard s pielawa harvard d pekker harvard r sensarma harvard

Doublon production rate depends on

propagation of doublons and holes

Retraceable Path Approximation Brinkmann & Rice, 1970

preliminary data

Experimental data

courtesy of D. Greif

Spectral Fn. of single hole

Doublon Production Rate


T kitagawa harvard s pielawa harvard d pekker harvard r sensarma harvard

Lattice modulation experiments. Sum rule

Ad(h) is the spectral function of a single doublon (holon)

T-independent ?

Sum Rule :

Simple model to include

temperature dependence

and trap: multiply

production rate by the

average fraction of

nearest neighbors

with opposite spins

preliminary data

courtesy of D. Greif


Ramsey interference in one dimensional systems

Ramsey Interference in one dimensional systems

  • Using quantum noise to study many-body dynamics


T kitagawa harvard s pielawa harvard d pekker harvard r sensarma harvard

One dimensional systems in condensed matter

Non-perturbative effects of interactions:

Absense of long range order

Electron fractionalization

GaAs/AlGaAs

Heterostructures

carbon

nanotubes

1d organics

Emphasis on equilibrium properties and linear response


T kitagawa harvard s pielawa harvard d pekker harvard r sensarma harvard

1D Ramsey Interferometry (Widera, et.al PRL 2008)

1d systems of ultracold atoms:

analysis of nonequilibrium dynamics

Time evolution of coherence in split condensates

S. Hofferberth et al., Nature (2007)


Introduction ramsey interference

Introduction:Ramsey Interference


T kitagawa harvard s pielawa harvard d pekker harvard r sensarma harvard

1

Working with N atoms improves

the precision by .

t

0

Ramsey interference

Atomic clocks and Ramsey interference:


Ramsey interference with bec

Ramsey Interference with BEC

Single mode

approximation

Gaussian distribution

of Sz

Spin squeezing: possible application

in quantum enhanced metrology

Sorensen, Moller, Cirac, Zoller, Lewensstein, …


Ramsey interference with 1d bec

Ramsey Interference with 1d BEC

1d systems in microchips

1d systems in optical

lattices

Two component BEC

in microchip

  • Ramsey interference in 1d tubes:

  • Widera et al.,

  • PRL 100:140401 (2008)

Treutlein et.al, PRL 2004


Ramsey interference in 1d a probe of many body dynamics

Ramsey Interference in 1d:a probe of many-body dynamics


Ramsey interference in 1d condensates

Ramsey interference in 1d condensates

Spin echo experiments

A. Widera, et al, PRL 2008

Only partial revival

after spin echo!

Expect full revival of fringes


T kitagawa harvard s pielawa harvard d pekker harvard r sensarma harvard

Spin echo experiments in 1d tubes

Single mode approximation does not apply.

Need to analyze the full model


Low energy effective hamiltonian for spin dynamics

Low energy effective Hamiltonianfor spin dynamics

Bosonization

Tomonaga-Luttinger Hamiltonian

19


Ramsey interference initial state

Small uncertainty in

Ramsey interference: Initial State

After p/2 pulse, spins point in x direction

Initial state: squeezed state infs

Wk determined from

Short distance cut-off at spin healing length

related argument in Bistrizer, Altman, PNAS (2008)


Ramsey interference in 1d time evolution

Ramsey interference in 1dTime evolution

Luttinger liquid provides good agreement with experiments.

A. Widera et al., PRL 2008. Theory: V. Gritsev

Technical noise could also

lead to the absence of echo

Need “smoking gun” signatures

of many-body decoherece


Distribution functions of ramsey amplitude

Distribution functionsof Ramsey amplitude


Probing spin dynamics through distribution functions

Distribution

Probing spin dynamics through distribution functions

Distribution function contains information about higher order correlations

Joint distribution function can

also be obtained


Interference of independent 1d condensates

Interference of independent 1d condensates

S. Hofferberth, I. Lesanovsky, T. Schumm, J. Schmiedmayer,

A. Imambekov, V. Gritsev, E. Demler, Nature Physics (2008)

Higher order correlation functions

probed by noise in interference


Joint distribution functions

Joint distribution functions

Short segments

|S|^2 does not changebut Sx decays

Long segments

both Sx and |S|^2 decay


Two regimes of spin dynamics

Two regimes of spin dynamics

Modes with λ>l leads to the decay of Sx but not |S|

Modes with λ<l leads to the decay of both Sx and |S|


Analytic solution for the distribution function

Analytic solution for the distribution function


Summary

Summary

  • Suggested unique signatures of the multimode decoherence of Ramsey fringes in 1d

  • Ramsey interferometer combined with study of distribution function is a useful tool to probe many-body dynamics

  • Joint distribution functions provide simple visualization of complicated many-body dynamics


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